The Historical Framework
So far, we have portrayed the mathematical practice of the Old Babylonian scribes and their teachers; inasmuch as this practice is located differently from ours in historical space, the investigation is certainly a contribution to the history of mathematics — but since it has not approached the development of the practice in question (not to speak of the motive forces of this development) it has not yet approached the history of Babylonian mathematics. The model was that of structural-functional anthropology rather than history.
KeywordsChapter VIII Problem Text Historical Framework Theme Text Historical Space
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- 346.Heyrup 1994: 45–87] is a more detailed analysis of the interplay between statal bureaucracy, scribal craft and culture, and the transformations of mathematics from the beginnings through the mid-second millennium, with extensive bibliography.Google Scholar
- 347.The “state” is understood here as a social system characterized by an at least three-tiered system of control and by extensive specialization of social roles — cf. [Wright and Johnson 1975] and [Hoyrup 1994: 48–51].Google Scholar
- 348.On the token system and its development, see [Schmandt-Besserat 1992]; the book may perhaps not be precise in all details — no pioneering work of this scope ever is; but Schmandt-Besserat has the indubitable merit to have discovered the longterm continuity of this system and to have investigated it in depth and breadth. Cf. the essay reviews by Peter Damerow  and Jöran Friberg  (to the critical points of the latter Schmandt-Besserat has some responses — personal communication).Google Scholar
- 349.Immediately preceding the invention of writing there is a short phase where tablets were produced on which only metrological notations but no word signs are found. Since the tablets are rarely found in original position, the chronological precedence of these “numerical tablets” is inferred, not independently established; but since the notations are clearly different from those of the protoliterate phase (and reflect experimentation and lack of established conventions rather than different conventions), the inference is convincing; see [Nissen, Damerow, and Englund 1993: 125–130].Google Scholar
- 350.Evidently, it makes no absolute sense to speak of integral units and subunits in a metrological system; the relative sense is constituted by the way the writing system deals with them.Google Scholar
- 351.A broad summary of fourth and third millennium mathematical techniques (including a description of the metrologies) can be found in [Nissen, Damerow, and Englund 1993] — the detailed information about the proto-literate phase can be found in [Damerow and Englund 1987]; for the administrative calendar, see [Englund 1988]. The conjectures about the development of the numerals are mine.Google Scholar
- 352.The protoliterate script had been logographic, deprived of phonetic and grammatical elements; documents were organized as schemes that corresponded to 314 Chapter VIII. The Historical Framework bureaucratic routines, and did not attempt to render sentences; the grammatical elements and incipient use of phonetic principles that begin to turn up around 2700 are indubitably Sumerian. If we dismiss fanciful ideas about foreign conquerors from Caucasus, Tibet, Thailand, etc. (of which there have been many, but never supported by the least evidence), it seems a natural assumption that the language spoken in the southern region remained unchanged, and that the language of protoliterate Uruk was thus an early Sumerian. Much in the structure of Sumerian suggests, however, that it may have developed locally from a creole spoken by enslaved populations in the late fourth millennium and then taken over by the minority of masters (as often happens in such situations when no metropolis can protect the original language of these). See [Heyrup 1992a1.Google Scholar
- 353.The sometimes heavy use of Sumerian word signs may mislead on this account, and have misled many workers into the belief that the whole complex of Old Babylonian mathematics was of Sumerian origin. With utterly few exceptions, however, the underlying grammatical structure is Akkadian; in the actual exceptions (see, for instance, note 281), the Sumerian grammar is either wrong and somehow home-made or suspiciously dependent on the grammar book (more so than in the Sumerian literary compositions and grammatical texts of the Old Babylonian age). The use of Sumerograms is no more proof of a Sumerian origin than the Vatican Latin dictionary is proof that the ancient Romans knew about railways, trade unions, and nuclear fission.Google Scholar
- 354.W 23273, cf. [Friberg 1993: 400].Google Scholar